In general, risers are made up of pipe sections that are butt joined by means of connectors. Documents FR-2,432,672, FR-2,464,426 and FR-2,526,517 disclose connectors for risers provided with auxiliary lines. These connectors are designed to withstand relatively low pressures because the BOPs arranged on the wellhead at the sea bottom limit the maximum pressure value in the riser. In fact, under well blowout control conditions, the BOPs are closed and the fluids circulate through the auxiliary lines. According to the prior art, indexing and locking in rotation the elements of these connectors is provided by the auxiliary lines.